Answer:
the radius = 15 cmStep-by-step explanation:
let r be the radius of the circle.
→ We know that in circle , the length of an arc
and the corresponding central angle are proportional.
180 corresponds to πr
120 corresponds to 10π
Then
[tex]\frac{\uppi r}{180} =\frac{10\uppi }{120}[/tex]
[tex]\Longrightarrow r=\frac{180\times 10\pi }{120\pi } =\frac{180}{12} =15[/tex]
How many rational numbers lie between any two fractions?
Answer:
Infinite number of rational numbers exist between any two distinct rational numbers. We know that a rational number is a number which can be written in the form of qp where p and q are integers and q =0.
I NEED HELP ASAP
A box has 1 red marble, 3 blue marbles, and 4 green marbles. Maya draws a blue marble randomly from the box, replaces it, and then draws another marble randomly. What is the probability of drawing 2 blue marbles in a row? Explain your answer.
Answer:
8
Step-by-step explanation:
each times she draws there is 3 blue marbles that she can pick so her chance of picking one blue marble out of the box is 3/8 hope i helped!
Answer: 3/8
Step-by-step explanation:
4 5/6 - 2 1/2
please help!
Answer:
2.33
Step-by-step explanation:
What type of function is f(x) = 2x³ - 4x² + 5? O Exponential O Logarithmic O Polynomial O Radical
Answer:
Polynomial
Step-by-step explanation:
⇒ It cannot be option 1 as y does not vary with an exponent
⇒ It cannot be option 2 as y does not relate to any logarithmic values of x
⇒ It cannot be a option 4 as there no irrational numbers under a root
⇒ Therefore it is a polynomial, as it is written in the form : y = ax³ + bx² + cx + d (cubic polynomial)
Can you help me please!!!!
Answer:
Irrational
Step-by-step explanation:
[tex]\sqrt{9}= 3[/tex]
3 × √3 = 3√3 which is irrational
Hope this helped and brainliest please
Product is multiplication:
√3 x √9 = 3√3 = 5.19615....
Because the fraction does not end, it is not rational.
Answer: Irrational
In any triangle ABC, if c=30°,b= 4, a=2 find A and B.
Using the Law of Cosines,
[tex]c^{2}=2^{2}+4^{2}-2(2)(4)(\sin 30^{\circ})\\\\c^{2}=12\\\\c=2\sqrt{3}[/tex]
Using the Law of Sines,
[tex]\frac{\sin A}{a}=\frac{\sin C}{c}\\\\\frac{\sin A}{2}=\frac{\sin 30^{\circ}}{2\sqrt{3}}\\\\\frac{\sin A}{2}=\frac{1}{4\sqrt{3}}\\\\\sin A=\frac{1}{2\sqrt{3}}\\\\A=\boxed{\sin^{-1} \left(\frac{1}{2\sqrt{3}} \right)}[/tex]
So, as angles in a triangle add to 180 degrees,
[tex]B=180^{\circ}-30^{\circ}-\sin^{-1} \left(\frac{1}{2\sqrt{3}} \right)\\\\B=\boxed{150^{\circ}-\sin^{-1} \left(\frac{1}{2\sqrt{3}} \right)}[/tex]
Simplify the expression 5^3 x 5^-5
A. 5^2
B. 1/5
C. 1/5^2
D. -52
[tex] {5}^{3} \: \times \: {5}^{ - 5} [/tex]
We first compute the product.[tex] {5}^{ - 2} [/tex]
We can transform the product into positive if we use this formula:[tex] \boxed{ {a}^{ - n} \: = \: \frac{1}{ {a}^{n} } }[/tex]
We apply it:[tex] {5}^{ - 2} \: = \: \boxed{ \bold{\frac{1}{ {5}^{2} } }}[/tex]
Answer:[tex]\text{Option C.} \: \boxed{ \bold{\frac{1}{ {5}^{2} } }}[/tex]
MissSpanishA square purple rug has a green square in the center. The side length of the green square is x inches. The width of the purple band that surrounds the green square is 3 in. What is the area of the purple band?
NEED ANSWER ASAP HELP
Given ABC with altitude h
Prove: sin(B)/b=sin(C)/c
Using the given information in the diagram, we have proven that sin(B)/b = sin(C)/c
Proving the Sine ruleFrom the question, we are to prove that sin(B)/b=sin(C)/c
Consider the right triangle with sides a, c, and h
Using SOH CAH TOA, we can write that
sin(B) = h/c
∴ h = c × sin(B) --------- (1)
Also,
Consider the other right triangle
Using SOH CAH TOA, we can write that
sin(C) = h/b
∴ h = b × sin(C) ---------- (2)
Equate equations (1) and (2)
That is,
c × sin(B) = b × sin(C)
This can then be expressed as
sin(B)/b = sin(C)/c
Hence, the given expression is proven as shown above
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What is the standard error of the sampling distribution of sample proportion?.
Answer:
√ (p(1-p) / n)
Step-by-step explanation:
Standard Error(SE) of the Sample Proportion: √ (p(1-p) / n). Note: as the sample size increases, the standard error decreases.
---Hope this helps you! Feel free to give feedback
Which equation is represented by the graph below?
←+
+
1 2 3 4 5 x
5
54
3.
2-
1
--5-4-3-2-11
-2
-3
The function of the curve is an exponential function. So, the function would be y = e^x.
What are exponential functions?When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function.
Their usual form is specified below. They are written in several such equivalent forms.
For example, [tex]y^x[/tex]
where a is a constant is an exponential function.
We can see that the curve of the function is decreasing constantly.
Thus, the function of the curve is an exponential function. So, the function would be y = e^x.
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Needing help with these 2 problems
Answer:
15) 3.2
17) 13.4
Step-by-step explanation:
To find the missing lengths, you need to use the Pythagorean theorem:
a² + b² = c²
In this form, "c" represents the length of the hypotenuse and "a" and "b" represent the lengths of the other two sides.
You are trying to find one of the side lengths (not the hypotenuse) in 15). To find the other length, you can plug the other values into the equation and simplify to find "b".
15) a = 4.1 c = 5.2
a² + b² = c² <----- Pythagreom Theorem
(4.1)² + b² = (5.2)² <----- Plug values in for "a" and "c"
16.81 + b² = 27.04 <----- Raise numbers to the power of 2
b² = 10.23 <----- Subtract 16.81 from both sides
b = 3.2 <----- Take the square root of both sides
You are trying to find the hypotenuse in 17). Since you have been given the lengths of the other sides, you can plug them into the equations and simplify to find "c".
17) a = 4.4 b = 12.7
a² + b² = c² <----- Pythagreom Theorem
(4.4)² + (12.7)² = c² <----- Plug values in for "a" and "b"
19.36 + 161.29 = c² <----- Raise numbers to the power of 2
180.65 = c² <----- Add
13.4 = c <----- Take the square root of both sides
Suppose the average age of family members is 34 with a standard deviation of 4. if 100 members of the community decided to have a summer outing bonding and relaxation, find the probability that the average of these members is less than 35?
Using the normal distribution, it is found that there is a 0.9938 = 99.38% probability that the average of these members is less than 35.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem, we have that the parameters are given as follows:
[tex]\mu = 34, \sigma = 4, n = 100, s = \frac{4}{\sqrt{100}} = 0.4[/tex].
The probability that the average of these members is less than 35 is the p-value of Z when X = 35, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{35 - 34}{0.4}[/tex]
Z = 2.5
Z = 2.5 has a p-value of 0.9938.
0.9938 = 99.38% probability that the average of these members is less than 35.
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Consider the graph of the linear function h(x) = -x + 5. Which could you change to move the graph down 3 units?
O the value of b to -3
the value of m to -3
the value of b to 2
O the value of m to 2
Intro
Done
Answer:
the value of b to 2
The value of b changes to 2.
The correct option is C.
What is Linear Equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
We have,
Equation: h(x) = -x + 5
Now, using the slope intercept form
y = mx + b
From which we get
m = -1 and b=5
Now, we need to move the graph 3 units down then we need to subtract given function by 3, we get
y = -x+5 -3
y = -x +2.
Here y-intercept is 2.
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Mickey drew a scale drawing of the room in his junior high building using the scale 1 centimeter (cm) - 1.5 meters (m). the office in his scale drawing measured 2.6 cm * 3.2 cm. what
are the actual dimensions of the office?
2.6 m x 3.2 m
1.7 m x 2.1 m
3.9 m x 4.8 m
4.1 m x 47 m
Answer:
3.9m x 4.8m
Step-by-step explanation:
1 cm = 1.5m
→ Multiply both sides by 2.6
2.6 cm = 3.9m
→ Multiply from the original statement, both sides by 3.2
3.2 cm = 4.8 m
→ Combine them
3.9m x 4.8m
Give your answer in terms of [tex]\pi \\[/tex]
The length of the band in terms of π is given by the expression:
L = 40mm + π*10mm
How to get the length of the band?
Remember that for a circle of diameter D, the circumference is:
C = π*D.
Now, if you look at the image, you can see that the length of the band will be equal to 4 times the diameter of the pencils (one time for each side). Plus 4 times one-fourth of the circumference of each pencil (for the four corners).
because the diameter is 10mm, the length of the band will be:
L = 4*10mm + 4*(π*10mm/4)
L = 40mm + π*10mm
This is the length of the band in terms of π.
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Complete the equations below. 15.3 ÷ 3 = tenths + 3 15.3÷ 3 = tenths 15.3 ÷ 3 =
The value of the complete equation is 5.1.
We have given the equation,
15.3 ÷ 3 = tenths + 3 15.3÷ 3 = tenths 15.3 ÷ 3
What is the equation?
An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Therefore we have,
[tex]15.3/3=15+0.3 \ tenths/3\\=5+0.1 \ tenths\\=5.1[/tex]
Therefore the value of the complete equation is 5.1.
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What conclusions can you draw from the first battles in the civil war?
How would I solve this?
Answer:
(-2, -2)
Step-by-step explanation:
the solution of the system of equation put simply is the point of intersection between the 2 lines
hence, the answer is (-2,-2)
A right circular cone is intersected by a plane that passes through the cone's
vertex and is perpendicular to its base, as in the picture below. What is
produced from this intersection?
A. A single line
B. A pair of intersecting lines
C. A point
D. A pair of parallel lines
Answer:
B. A pair of intersecting lines
Step-by-step explanation:
The attached image can give you an idea of what you get when a plane perpendicular to the base of a cone intersects the vertex of the cone.
__
In the problem statement here, we assume a double-napped cone with no defined base. That means the lines of intersection with the sides of the cone will meet at the vertex point and extend indefinitely in either direction.
The intersection is a pair of intersecting lines.
What is the area of the triangle below?
O27 square units
O 45 square units
O 54 square units
20
A triangle is a 2-D shape that has 3 sides and angles. The area of the triangle below is 27 square units
Area of a triangleA triangle is a 2-D shape that has 3 sides and angles
In order to determine the area of the shape, we will determine the area of the square circumscribing it first;
Area of the square = 10 * 9 =90 square units
Find the area of the two right triangles
Area of the right triangles = 0.5(10 * 9) + 0.5(9 * 4)
Area of the right triangles = 45 + 18
Area of the right triangles = 63 square units
Take the difference
Area of the given triangle = 90 - 63 = 27 square units
Hence the area of the triangle below is 27 square units
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The area of a rectangular parking lot is 7081 m²
If the length of the parking lot is 97 m, what is its width?
Step-by-step explanation:
So the question is easy ....The thing that you need to do here is ...You should divide area by length....and you will get your answer....
Area of square = l²Area of rectangle = l × bArea of rectangular parking lot = 7081 m²
length of parking lot = 97 m
Width = ?
Now,
Area = l × b
7081 = 97 × b
7081 / 97 = b
b = 73 m
Hence the width is 73 m....
At the stadium, there are eight lines for arriving customers, each staffed by a single worker. The arrival rate for customers is 190 per minute and each customer takes (on average) 2 seconds for a worker to process. The coefficient of variation for arrival time is 1.2 and the coefficient of variation for service time is 1.5. (1) How much time (in seconds) will an average customer spend in queue
Answer:
3.287 Customers
Step-by-step explanation:
Interarrival time (a) = 60 seconds per minute / 190 customers per minute = 0.316 seconds.
Utilization = p / (a × m) = 2 / (0.316 × 8) = 0.792.
Number in queue = Tq / a = 1.038 / 0.316 = 3.287 customers.
What is the equivalent to 8 ounces?
Answer:
16 Tablespoons
Step-by-step explanation:
PLEASE HELP PLEASE ANSWER QUICKLY IM RATING 5 STAR AND BRAINLIEST IM LIKE BEGGING FOR HELP ON THIS QUESTION PLEASE ⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️
Answer:
See below
Step-by-step explanation:
Sine function would be easiest
in a right triangle sin = opposite leg / hypotenuse
sin 57 = 10.8 / x
then x = 10.8 / sin 57 then x = 12.88 units
Find the LCM of 16x² and 40x5
Answer:
The LCM of 16x^2 and 40x^2 is 80x^5
:) Good Luck
Step-by-step explanation:
calculate 20% of R400
Answer:
80Step-by-step explanation:
400: 100 you find 1% you multiply it by 20 and you have 20%
400 : 100 * 20 =
4 * 20 =
80
How many solutions exist for the system of equations graphed below?
a.) none
b.) one
c.) two
d.) infinitely many
Answer:
one
Step-by-step explanation:
When a system of equations is graphed, the solution is the coordinate that is plotted at the intersection of the two lines.
If the two lines cross once, there is only one solution.
If the two lines are on top of each other then there are infinitely many solutions.
If the two lines are parallel ( and never touch ) then there are no solutions
By looking at the graph we notice the two lines intersect once. So we can conclude that there is only one solution.
Explore
create a dot plot of a sample of the population whose
mean is the same as the population mean.
your sample should have more than six, but fewer than
20 data points.
count
number
2
10
12
8
hean
10
12
8
mean
934
The 2nd dot plot in the attachment represents the dot plot that has the same sample mean as the population mean
How to create the dot plot?The dot plot that completes the question is added as an attachment.
Start by calculating the mean of the data plot using:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
Substitute the values on the dot plot
[tex]\bar x = \frac{2*1+3*3+4*2+5+6*3+7*5+8*2+9*4+11*2+12*2}{25}[/tex]
[tex]\bar x = 7[/tex]
This means that the population mean of the dot plot is 7
Next, we create another dot plot that has the same mean as 7.
There are no direct rules to this, so we make use of the trial by error method.
After several attempts, we have the following frequency table:
Data point Frequency
2 1
3 2
4 0
5 4
6 5
7 2
8 5
9 0
10 2
12 3
The mean of the frequency table is:
[tex]\bar x = \frac{2 * 1 + 3 * 2 + 4 * 0 + 5 * 4 + 6 * 5 + 7 * 2 + 8 * 5 + 9 * 0 + 10 * 2 + 12 * 3}{1+2+0+4+5+2+5+0+2+3}[/tex]
Evaluate
[tex]\bar x = \frac{168}{24}[/tex]
Evaluate the quotient
[tex]\bar x = 7[/tex]
This means that the sample mean is 7 (same as the population mean)
Lastly, we represent the frequency table using a dot plot (the 2nd dot plot in the attachment)
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What is the value of 4x-7 when x = 4?
O 1
09
O 16
23
Answer:
9
Step-by-step explanation:
Given expression: 4x - 7
To determine a numerical value of the provided expression, when x = 4, simply substitute the value of x into the expression and simplify it using the order of operations (PEMDAS). Work has been shown below.
[tex]\implies 4x - 7[/tex][tex]\implies 4(4) - 7 \ \ \ \ \ \ [\text{Substituting the value of x}][/tex]Simplify the expression using PEMDAS:The PEMDAS stands for:
ParenthesesExponentsMultiplicationDivisionAdditionSubtractionFirst - LastAccording to the PEMDAS, it is required to simplify the expression using multiplication (M in PEMDAS) firsthand, as there are no parentheses (P in PEMDAS) and exponents (E in PEMDAS). Thus, we get the following:
Please refer to underlined text for simplification of that expression.
[tex]\implies 4 \times 4 - 7[/tex][tex]\implies \underline{4 \times 4} - 7}[/tex][tex]\implies {16 - 7}[/tex]Clearly, we can see that division (D in PEMDAS) and addition (A in PEMDAS) is not occurring in the expression. Therefore, we will need to subtract the two terms (16 and 7). Thus, we get the following simplified term:
[tex]\implies \underline{16 - 7}[/tex][tex]\implies \boxed{9}[/tex]Therefore, the value of 4x - 7, when x = 4, is 9.
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